- Email: [email protected]
Simulation of char and propane combustion in a fluidized bed by extending DEM–CFD approach
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Proceedings of the
Proceedings of the Combustion Institute 33 (2011) 2701–2708
Combustion Institute www.elsevier.com/locate/proci
Simulation of char and propane combustion in a fluidized bed by extending DEM–CFD approach Daoyin Liu, Xiaoping Chen *, Wu Zhou, Changsui Zhao School of Energy and Environment, Southeast University, Nanjing 210096, China Available online 9 August 2010
Abstract The simultaneous combustion of char and propane in a fluidized bed is investigated numerically. A comprehensive discrete element method (DEM)–CFD model is developed, which takes into account particle-scale heat transfer, homogeneous and heterogeneous reactions, as well as hydrodynamics of dense gas–solid flow in fluidized beds. The coupling between the gas continuity and heterogeneous reactions is addressed which has been neglected in previous studies for the comprehensive DEM–CFD model. The combustion behaviors of the char particles and combustible gases are discussed with existed experimental findings. The model predicts the gaseous fuel reduces the char combustion rate and the negative effect is more evident with higher bed temperatures or highly reactive chars, which is consistent with the “surprising” experimental finding by Hesketh and Davidson [24]: the char combustion rate decreases as the temperature rises. The calculated profiles of gas species indicate the combustible gases can be burned significantly above the bed surface, in rising bubbles, or inside the emulsion phase, mainly depending on the bed temperature. A further insight into the simulation results shows the local heat source generated from the homogeneous reactions fluctuates with gas volume fraction, indicating the gas reaction is highly related with bubbles, which agrees with the optical measurements by Zukowski et al. [26]. The developed comprehensive DEM–CFD model provides detailed local information as well as macro structures. It can play an important role in a multiscale strategy for fluidized bed combustion. Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Fluidized bed combustion; Char; Propane; DEM-CFD model; Multiscale
1. Introduction In a fluidized bed combustor, details of the local phenomena, e.g., particle motion and heating up, fuel devolatilization, volatile matter combustion, and char reaction with O2 diffused from bubble phase, directly influence the macroscopic phenomena of the combustion process. However, their scales are greatly separated, which results in *
Corresponding author. Fax: +86 25 83793453. E-mail address: [email protected] (X. Chen).
detailed modeling of the entire combustion process in a fluidized bed being a challenging task. Peters [1] has addressed that combustion is a multiscale process, and researchers should pay attention on interactions of the phenomena at different scales in the modeling study. As regards dense gas–solid flow dynamics in fluidized beds, several researchers [2–4] suggested a similar multiscale modeling strategy using different models from fine to coarse levels, e.g., direct numerical simulation (DNS), discrete element model (DEM) combined with CFD, and two-fluid model (TFM). In the DEM–CFD model, each
1540-7489/$ - see front matter Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2010.06.070
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individual particle is tracked and gas phase dynamic is solved by Navier-Stokes equations. It can link dynamic structures at different scales: given micro laws for particle–particle and gas– particle interactions, macro flow structures at system scale can be predicted. In a review of the DEM–CFD model, Deen et al. [5] showed the model is a powerful tool for complex dense gas– solid system, and it can play an important role in the multiscale strategy for multiphase flow. The DEM–CFD model has been used for validating drag relations derived from the DNS simulations, or testing the assumption of velocity distribution and other closures used in the TFM simulations. At the end of the review, they also suggested incorporation of other processes, such as particle heating up and reaction, into the DEM–CFD model. The DEM–CFD model has gained significant development since early 1990s [5,6]. It can predict detailed characteristics inside fluidized beds, e.g., local porosity, gas and particle velocities. The detailed simulation results, together with the reliable data from advanced experimental techniques, are leading to a better understanding on fluidized beds hydrodynamics [7]. Meantime, the detailed results of hydrodynamics provide information as input parameters for modeling of gas–solid heat transfer and heterogeneous/homogeneous reactions. Thus, it is a natural way to incorporate these processes into the DEM–CFD model. In the present work, the validated submodels of heat transfer and combustion processes from the literature have been incorporated into the DEM–CFD model. The developed model has realized a detailed description of the coupled effects of multiphase flow dynamics, heat transfer, and combustion processes. In a multiscale strategy for the long term, the model will provide fundamental closures for coarse grained models designed for large-scale combustors. It should be mentioned that in recent years a few efforts have been devoted to extend the DEM–CFD model. Examples are Refs. [8–12]. They integrated particle-scale heat transfer models with the DEM–CFD model, and obtained encouraging simulation results. For chemical reaction problems, Kaneko et al. [13] extended DEM– CFD model by introducing particle polymerization reaction rate and energy balance to study gas phase olefin polymerization. Limtrakul et al. [14] integrated a catalytic gas reaction and mass conservation of chemical species with the DEM– CFD model, to study decomposition of ozone on oxide catalyst in a isothermal spouted bed reactor. Recently, Wu et al. [15] incorporated four-lump gas phase reactions catalyzed by solid, and conservations of energy and chemical species, to simulate gas–solid reacting flows in riser or downer reactors. For modeling of combustion in a fluidized bed, heterogeneous reactions, as well
as homogeneous reactions and heat transfer, should be considered. Rong and Horio [16] incorporated char combustion into DEM simulation. Zhou et al. [17] built such a comprehensive DEM–CFD model for simulating coal combustion in a fluidized bed. Oevermann et al. [18] also built a comprehensive model of this kind for simulating wood gasification in a fluidized bed. The active contribution of these works is that they demonstrated the extended DEM–CFD model, which describes the complex physical and chemical behaviors at particle-scale in fluidized bed combustors/gasifiers, can provide detailed information for an increasing understanding on fluidized bed combustion/gasification. The extended DEM–CFD model, developed in this paper for simulating fluidized bed combustion, is somewhat different from the previous works. In our model, the source term of the gas continuity equation is rationalized which is determined by heterogeneous reactions, instead of zero in the previous works [16–18]. The model simulates simultaneous combustion of char and propane in a fluidized bed. The combustion behaviors of char and combustible gases are discussed and comparisons with existed experimental findings are highlighted. 2. Mathematical formulation The model described is an extension of the hydrodynamic DEM–CFD model [5]. It includes models for hydrodynamics, heat transfer, and heterogeneous and homogeneous reactions. The coupling between the gas continuity and heterogeneous reactions is addressed. 2.1. Hydrodynamic DEM–CFD model In the DEM–CFD model, each individual particle is tracked by Newtonian equation. For each particle, the linear and angular momentum equations are mi Ii
N X dvi ¼ V i rpg þ Fd þ Fg þ ðFij;n þ Fij;t Þ ð1Þ dt j¼1
N N X dwi X ðTij;t Þ ¼ ðRj nij Fij;t Þ ¼ dt j¼1 j¼1
ð2Þ
where i represents a single particle, j the particles contacted with particle i, m, V, I, R, v, and w the particle mass, volume, inertia moment, radius, linear velocity, and angular velocity, respectively, rpg the local pressure drop, Fd the drag force, Fg the gravitational force, Fij;n and Fij;t the normal and tangential components of the contact force from particle j to i, and Tij;t the torque. The contact force is calculated according to a linear spring-dashpot model where the force is a
D. Liu et al. / Proceedings of the Combustion Institute 33 (2011) 2701–2708
function of particle overlap and relative velocity. Details of the contact force model can be referred to Ref. [5]. Since a gas–solid system usually has a large number of particles, it is essential to optimize the strategy of particle collision detection. The present model employs the cell list and neighbor list techniques to speed up the search for particle collision. The drag force, Fd in Eq. (1), is calculated by Fd ¼
V ib ðu vi Þ ð1 eg Þ
ð3Þ
where u is the local gas velocity, eg the local gas volume fraction, and b inter-phase momentum transfer. The drag models frequently used in gas–solid fluidized beds [7], Ergun, Wen, Yu, De Felice, and Beetstra et al. models, are implemented in the developed model. During the present simulation, Ergun, Wen, and Yu drag model is adopted. The gas phase is treated as continuum and described by the volume-averaged Navier-Stokes equations. Mass and momentum conservations are @ ðeg qg Þ þ r ðeg qg uÞ ¼ S g @t @ ðeg qg uÞ þ r ðeg qg uuÞ @t ¼ eg rpg þ r ðeg sg Þ þ eg qg g Sm
ð4Þ
ð5Þ
where qg is the gas density, sg the gas viscous stress tensor, S g the gas mass source due to heterogeneous reactions, Sm the gas momentum source due to inter-phase interaction. For dense gas–solid flows in fluidized beds, two-way coupling is required. According to Newtonian third law, Sm in a fluid cell is determined by adding up the drag force of the particles located in the fluid cell. Sm ¼
Np 1 X
V cell
Fd
ð6Þ
k¼1
where V cell is the volume of the fluid cell. In the hydrodynamic DEM–CFD model, S g in Eq. (4) is set to zero. When it is extended to model of reacting gas–solid systems involved with heterogeneous reactions, S g should not be zero. However, the previous works [16–18] neglected this effect. In our model, S g due to heterogeneous reactions is considered which is introduced in the following. 2.2. Heat transfer The heat balance for an individual particle is given below: mi C p;i
dT i ¼ Qcv þ Qpp þ Qrad þ QR dt
ð7Þ
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where Qcv ; Qpp ; Qrad ; and QR represent gas– particle convective, particle–particle conduction, radiation heat transfer, and heterogeneous chemical reactions, respectively. Qcv is calculated by Qcv ¼ hcv Ai ðT g T i Þ, where the heat transfer coefficient hcv is determined by Ranz and Marshall correlation [9,17]. Qpp is calculated by the method used in Ref. [10]. For simplicity, Qrad is not considered in the present model. The conservation equation for the gas energy is @ ðeg qg C pg T g Þ þ r ðeg qg C pg uT g Þ @t ¼ r ðeg k g rT g Þ þ S Q;cv þ S Q;R þ S h
ð8Þ
where T g is the gas temperature, C pg the gas capacity, k g the gas thermal conductivity, S Q;cv the heat source due to gas–particle convective heat transfer, S Q;R the heat source due to chemical reactions, S h the heat transported by mass source of S g in Eq. (4). S Q;cv is calculated in a similar way of Sm in Eq. (5), S Q;cv ¼
Np 1 X
V cell
Qcv
ð9Þ
k¼1
S Q;R is determined by heat release of chemical reactions. S h is determined by the formation enthalpies carried along with the inter-phase transferred mass of S g in Eq. (4). The momentum transfer due to S g is not calculated since it is negligible. 2.3. Heterogeneous reactions Char particle oxidation reaction is considered. CO and CO2 are produced according to the following equation: k eff
C þ 0:5ð1 þ gÞO2 !ð1 gÞCO þ gCO2
ð10Þ
where g denotes the proportion of CO2 and its value is determined according to the experimental results by Refs. [19,20]. The “Shrinking Core – Constant Particle Size” model is adopted, in which the reaction surface moves into the char particle, leaving behind an ash layer. Thus, the effective char particle oxidation rate (k eff ) is controlled by three steps: diffusion of gaseous reactant from gas phase to the particle surface, diffusion of gas through the ash layer, and reaction of gas with char at the core surface. Due to a short simulation of 15 s in the present work, the variation in char core diameter is negligible, which permits that the resistance of diffusion of gas through the ash layer is neglected. Therefore, the effective char particle combustion rate is controlled by 1 1 1 ¼ þ k eff k kin hm
ð11Þ
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where k kin is kinetic rate at the char particle surface, and hm the mass transfer coefficient to particle surface. k kin is calculated by Arrhenius-type correlation [21]. k kin ¼ 595T p expðEA =Ru T p Þ
ð12Þ
hm is calculated by particle Sherwood number which is determined according to the study by Ref. [22]. The mass balance equation for the char particle is dmi ¼ k eff Ai C O2 dt
ð13Þ
where Ai is the particle surface area, and C O2 the molar concentration of O2. The mass balance for the gas species i is @ ðeg qg Y i Þ þ r ðeg qg uY i Þ @t ¼ r ðDi rY Þ þ S Yi
ð14Þ
where Y i is the mass-fraction of gas species i, Di its diffusion coefficient, and S Yi the net production rate of species i due to heterogeneous and homogeneous reactions. The heterogeneous reaction of Eq. (10) alters the gas continuity, and the mass source of Eq. (4) is determined by S g ¼ MW O2 x_ O2 þ MW CO x_ CO þ MW CO2 x_ CO2
ð15Þ
where MW O2 ; MW CO ; and MW CO2 are the molecular weight of O2, CO and CO2, respectively, and x_ O2 ; x_ CO ; and x_ CO2 the net volumetric production rate of O2, CO and CO2 in a fluid cell, respectively, which are calculated by mapping the char particle reaction to the fluid cells.
3.1. Computational condition All simulations are performed on a pseudo-3D fluidized bed with bed thickness of one particle diameter. The gas is introduced uniformly at the bed bottom and flows out of the bed at the top. At the gas inlet, the gas velocity and temperature are specified. At the outlet, the pressure-outlet boundary condition is adopted. At the walls, the no-slip wall condition for the gas phase is assumed and the heat flux zero. Table 1 lists details of the parameters for the simulated system. In different simulation cases, (a) two kinds of chars with activation energy in Eq. (12), EA = 149 106 J/kmol, 125 106 J/kmol, denoted as Char A and B, (b) three levels of temperature for initial and boundary conditions, T0 = 1123, 1173, 1223 K, (c) two kinds of mixtures of gas inlet, with propane-premixed (YO2 = 23%, YC3H8 = 3.74%, and YN2 = 73.26%) and without propane (YO2 = 23% and YN2 = 77%), denoted as gas A and B, are employed. In together, 12 cases are simulated. In all cases, both the CFD and DEM time steps are 0.0001 s. The gas–solid flow without chemical reactions is solved first. After basic flow pattern is established, the models of heat transfer and chemical reactions are activated, and the char particles located in the freeboard are freed. Then the simulation is performed for another physical 15 s. In the following sections, we present the combustion behaviors of the char particles and combustible gases, respectively, in comparison with findings from experimental studies in the literature. 3.2. Behaviors of char particles Figure 1 shows snapshots of the mixing pattern of the char particles for a typical condition (Char
2.4. Homogeneous reactions Propane (C3H8) combustion is considered. The reaction scheme adopts the four-step global kinetic mechanism proposed by Hautman et al. [23] C3 H8 ! 1:5C2 H4 þ H2 C2 H4 þ O2 ! 2CO þ 2H2 CO þ 0:5O2 ! CO2 H2 þ 0:5O2 ! H2 O
3. Results and discussion
ð16Þ ð17Þ ð18Þ ð19Þ
where the reaction rates and kinetic parameters are taken from Ref. [23]. The reaction rates, expressed as power functions of species molar concentration, may be infinite during computing. Program is designed to avoid such numerical problems. These stiff chemistry source terms are solved by the Runge–Kutta algorithm.
Table 1 The values of parameters for the simulation system. Bed size CFD cell size
16 80 cm2 0.8 1.6 cm2
Sand particle Diameter Number Density
1.5 mm 11,000 2600 kg/m3
Char particle Diameter Number Density Carbon/ash
1.5 mm 300 2200 kg/m3 70/30%
Gas Minimum fluidization velocity Inlet gas velocity
0.972 m/s at 1123 K 4 m/s for all cases
D. Liu et al. / Proceedings of the Combustion Institute 33 (2011) 2701–2708
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Fig. 1. Snapshots at different times of mixing patterns for a typical condition (Char A, YC3H8 = 3.74%, T0 = 1173 K). The char particles are amplified by a factor of 5 for better observation. The yellow (weak color) particles represent bed particles, while black (strong color) particles chars. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
A, YC3H8 = 3.74%, T0 = 1173 K). The char particles located in the upper bed are freed at 2 s and fall down onto the dense bed surface, where the bubbles burst causing a strong solids back mixing. Then the chars move into the dense bed and follow the movement of the bed particles driven by the bubbles. After about 9 s, a well-mixed state of the chars is reached. The computation clearly demonstrates the intense solids mixing which is regarded as a special characteristic of fluidized beds. Figure 2 shows the total mass of carbon as a function of time under different conditions. The total mass of carbon is calculated by summing up the carbon mass contained in each of the char particles. In Fig. 2a, under propane-free atmosphere the reaction rate of Char A increases with increase in the bed temperature, and it decreases by adding propane into the gas. In Fig. 2b, for Char B under propane-free atmosphere its reaction rate keeps almost constant with increase in the bed temperature, while the reaction rate also decreases by adding propane into the gas. For better comparison of the results shown in Fig. 2, the total consumption mass of carbon related to its combustion time is calculated, yielding the average values of the char reaction rate. Figure 3 presents the char reaction rate under different conditions considered in Fig. 2. The reaction rate of Char B is much larger than that of Char A. Again, it can be clearly seen that under propane-free atmosphere the combustion rate of Char B keeps almost constant while Char A increases as the temperature rises. It indicates the reaction of Char B, with a lower value of activation energy, is controlled by mass transfer process. For both the chars, their combustion rates
Fig. 2. Total mass of carbon with time for various conditions. The total mass of carbon is calculated by summing up carbon mass within each individual char particle.
are decreased by premixing propane with the gas, because the propane competes for O2 with
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Fig. 3. Combustion rate of carbon for various conditions, calculated according to the data in Fig. 2.
the chars. Hesketh and Davidson [24] also observed the phenomena in their experimental investigations. Furthermore, the negative effect of the propane on the char reaction rate is more evident for Char B or at higher bed temperatures. A higher temperature promotes combustible gases to burn, but does not promote combustion of Char B since its reaction is controlled by mass transfer process. Thus, more amount of O2 is consumed by combustible gases within the bed at the higher temperature, reducing O2 available for the chars. Consequently, it happens that, although a bit of surprise at first glance, the combustion rate of Char B decreases as the bed temperature increases under propane-premixed atmosphere, which was found by Hesketh and Davidson [24]. 3.3. Behaviors of combustible gas The detailed combustion behaviors of gases can also be examined conveniently from the simulation results. An example is shown in Figure 4. It plots the mass-fraction profiles of gas species
Fig. 4. Gas species mass-fraction profiles along the bed height at 12 s for a typical condition (Char A, YC3H8 = 3.74%, T0 = 1173 K).
along the bed height at 12 s for the condition (Char A, YC3H8 = 3.74%, T0 = 1173 K). The combustion of C3H8 is almost completed below the height of 0.4 m. Within the reaction zone of C3H8, the reactants (C3H8 and O2) decrease along the height, the main product (CO2) increases, and the intermediate species (C2H4 and CO) first reach their peaks and then decrease. The presented results of the mass-fraction profiles of gas species are reasonable. Figure 5 compares the mass-fraction profiles of the main gas species (O2 and CO2) at different temperatures with Char A. As expected, the mass-fraction of O2 decreases as the temperature rises at the same bed height within the reaction zone of C3H8. It also gives an explanation for the variation of the char reaction rate presented in Fig. 3: O2 is consumed more within the dense bed as the temperature rises, leading to a decreased reaction rate of the char particles. The distribution of gaseous fuel combustion in fluidized beds has been investigated extensively [25,26]. In various experimental investigations, it seems that volatile combustion can take place significantly either above the bed surface, in rising bubbles, or inside the emulsion phase, which depends on the bed temperature [25]. Figure 6 plots the heat source generated from gas combustion for the conditions considered in Fig. 5. In the case of T0 = 1223 K, the heat source is intense within the dense bed, indicating the combustible gases are almost burned completely within a short distance above the distributor. For case T0 = 1173 K, a significant fraction of heat is released just above the bed surface, indicating less amount of gases are burned within the dense bed. When the temperature is further decreased, for case T0 = 1123 K, the phenomenon of intense heat release above the bed surface is more evident. Zukowski et al. [26] presented a insight into combustion of gaseous fuel in a fluidized bed. They obtained temperature fields in a fluidized
Fig. 5. Main gas species mass-fraction profiles of O2 and CO2 along height at 12 s at different temperatures of T0 = 1123, 1173, and 1223 K.
D. Liu et al. / Proceedings of the Combustion Institute 33 (2011) 2701–2708
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with bubbles. Figure 7a shows the instantaneous fluctuations of gas volume fraction at a computing cell, x = 7.6 cm and y = 5.6 cm, for the condition (Char A, YC3H8 = 3.74%, T0 = 1173 K); Fig. 7b accordingly shows the instantaneous heat source generated from two phase heat transfer, heterogeneous reactions, and homogeneous reactions. From the local structure, it can be found that the local heat source generated from the homogeneous reaction is dominant, and it fluctuates with gas volume fraction, suggesting the gas reaction is highly related with bubbles, which agrees with the visual measurements by Zukowski et al. [26]. 4. Conclusions Fig. 6. Contours of heat source generated from gas combustion at 12 s at different temperatures of T0 = 1123, 1173, and 1223 K.
bed burning a propane–air mixture by visual recording and RGB analysis, providing the direct proof that the local temperatures are associated
1. A comprehensive DEM–CFD model is developed for fluidized bed combustion. The model takes into account particle-scale heat transfer, homogeneous and heterogeneous reactions, as well as hydrodynamics of dense gas–solid flow in fluidized beds. The coupling between the gas continuity and heterogeneous reactions is addressed. 2. The developed model is used to simulate char and propane combustion in a fluidized bed. The phenomena observed from the simulation results are satisfying in various respects, e.g., (a) combustible gases reduce char combustion rate, especially for conditions with higher bed temperatures or highly reactive chars; (b) gas combustion takes place significantly above the bed surface, in rising bubbles, or inside the emulsion phase, depending on the bed temperature. 3. The results presented in this work clearly indicate the comprehensive DEM–CFD model can provide detailed local information as well as the macro structures at fluidized bed scale. It can play an important role in a multiscale strategy for fluidized bed combustion. Acknowledgments Financial supports of this work by National Key Technology R&D Program (2006BAA03 B02-10), the High-tech Research and Development Program of China(2009AA05Z311), and the Scientific Research Foundation of Graduate School of Southeast University are gratefully acknowledged. References
Fig. 7. Local fluctuations of instantaneous gas volume fraction and heat source due to two phase heat transfer, heterogeneous and homogeneous reaction, for a typical condition (Char A, YC3H8 = 3.74%, T0 = 1173 K) at a computing cell whose center position is x = 7.6 cm, y = 5.6 cm.
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Proceedings of the
Proceedings of the Combustion Institute 33 (2011) 2701–2708
Combustion Institute www.elsevier.com/locate/proci
Simulation of char and propane combustion in a fluidized bed by extending DEM–CFD approach Daoyin Liu, Xiaoping Chen *, Wu Zhou, Changsui Zhao School of Energy and Environment, Southeast University, Nanjing 210096, China Available online 9 August 2010
Abstract The simultaneous combustion of char and propane in a fluidized bed is investigated numerically. A comprehensive discrete element method (DEM)–CFD model is developed, which takes into account particle-scale heat transfer, homogeneous and heterogeneous reactions, as well as hydrodynamics of dense gas–solid flow in fluidized beds. The coupling between the gas continuity and heterogeneous reactions is addressed which has been neglected in previous studies for the comprehensive DEM–CFD model. The combustion behaviors of the char particles and combustible gases are discussed with existed experimental findings. The model predicts the gaseous fuel reduces the char combustion rate and the negative effect is more evident with higher bed temperatures or highly reactive chars, which is consistent with the “surprising” experimental finding by Hesketh and Davidson [24]: the char combustion rate decreases as the temperature rises. The calculated profiles of gas species indicate the combustible gases can be burned significantly above the bed surface, in rising bubbles, or inside the emulsion phase, mainly depending on the bed temperature. A further insight into the simulation results shows the local heat source generated from the homogeneous reactions fluctuates with gas volume fraction, indicating the gas reaction is highly related with bubbles, which agrees with the optical measurements by Zukowski et al. [26]. The developed comprehensive DEM–CFD model provides detailed local information as well as macro structures. It can play an important role in a multiscale strategy for fluidized bed combustion. Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Fluidized bed combustion; Char; Propane; DEM-CFD model; Multiscale
1. Introduction In a fluidized bed combustor, details of the local phenomena, e.g., particle motion and heating up, fuel devolatilization, volatile matter combustion, and char reaction with O2 diffused from bubble phase, directly influence the macroscopic phenomena of the combustion process. However, their scales are greatly separated, which results in *
Corresponding author. Fax: +86 25 83793453. E-mail address: [email protected] (X. Chen).
detailed modeling of the entire combustion process in a fluidized bed being a challenging task. Peters [1] has addressed that combustion is a multiscale process, and researchers should pay attention on interactions of the phenomena at different scales in the modeling study. As regards dense gas–solid flow dynamics in fluidized beds, several researchers [2–4] suggested a similar multiscale modeling strategy using different models from fine to coarse levels, e.g., direct numerical simulation (DNS), discrete element model (DEM) combined with CFD, and two-fluid model (TFM). In the DEM–CFD model, each
1540-7489/$ - see front matter Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2010.06.070
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individual particle is tracked and gas phase dynamic is solved by Navier-Stokes equations. It can link dynamic structures at different scales: given micro laws for particle–particle and gas– particle interactions, macro flow structures at system scale can be predicted. In a review of the DEM–CFD model, Deen et al. [5] showed the model is a powerful tool for complex dense gas– solid system, and it can play an important role in the multiscale strategy for multiphase flow. The DEM–CFD model has been used for validating drag relations derived from the DNS simulations, or testing the assumption of velocity distribution and other closures used in the TFM simulations. At the end of the review, they also suggested incorporation of other processes, such as particle heating up and reaction, into the DEM–CFD model. The DEM–CFD model has gained significant development since early 1990s [5,6]. It can predict detailed characteristics inside fluidized beds, e.g., local porosity, gas and particle velocities. The detailed simulation results, together with the reliable data from advanced experimental techniques, are leading to a better understanding on fluidized beds hydrodynamics [7]. Meantime, the detailed results of hydrodynamics provide information as input parameters for modeling of gas–solid heat transfer and heterogeneous/homogeneous reactions. Thus, it is a natural way to incorporate these processes into the DEM–CFD model. In the present work, the validated submodels of heat transfer and combustion processes from the literature have been incorporated into the DEM–CFD model. The developed model has realized a detailed description of the coupled effects of multiphase flow dynamics, heat transfer, and combustion processes. In a multiscale strategy for the long term, the model will provide fundamental closures for coarse grained models designed for large-scale combustors. It should be mentioned that in recent years a few efforts have been devoted to extend the DEM–CFD model. Examples are Refs. [8–12]. They integrated particle-scale heat transfer models with the DEM–CFD model, and obtained encouraging simulation results. For chemical reaction problems, Kaneko et al. [13] extended DEM– CFD model by introducing particle polymerization reaction rate and energy balance to study gas phase olefin polymerization. Limtrakul et al. [14] integrated a catalytic gas reaction and mass conservation of chemical species with the DEM– CFD model, to study decomposition of ozone on oxide catalyst in a isothermal spouted bed reactor. Recently, Wu et al. [15] incorporated four-lump gas phase reactions catalyzed by solid, and conservations of energy and chemical species, to simulate gas–solid reacting flows in riser or downer reactors. For modeling of combustion in a fluidized bed, heterogeneous reactions, as well
as homogeneous reactions and heat transfer, should be considered. Rong and Horio [16] incorporated char combustion into DEM simulation. Zhou et al. [17] built such a comprehensive DEM–CFD model for simulating coal combustion in a fluidized bed. Oevermann et al. [18] also built a comprehensive model of this kind for simulating wood gasification in a fluidized bed. The active contribution of these works is that they demonstrated the extended DEM–CFD model, which describes the complex physical and chemical behaviors at particle-scale in fluidized bed combustors/gasifiers, can provide detailed information for an increasing understanding on fluidized bed combustion/gasification. The extended DEM–CFD model, developed in this paper for simulating fluidized bed combustion, is somewhat different from the previous works. In our model, the source term of the gas continuity equation is rationalized which is determined by heterogeneous reactions, instead of zero in the previous works [16–18]. The model simulates simultaneous combustion of char and propane in a fluidized bed. The combustion behaviors of char and combustible gases are discussed and comparisons with existed experimental findings are highlighted. 2. Mathematical formulation The model described is an extension of the hydrodynamic DEM–CFD model [5]. It includes models for hydrodynamics, heat transfer, and heterogeneous and homogeneous reactions. The coupling between the gas continuity and heterogeneous reactions is addressed. 2.1. Hydrodynamic DEM–CFD model In the DEM–CFD model, each individual particle is tracked by Newtonian equation. For each particle, the linear and angular momentum equations are mi Ii
N X dvi ¼ V i rpg þ Fd þ Fg þ ðFij;n þ Fij;t Þ ð1Þ dt j¼1
N N X dwi X ðTij;t Þ ¼ ðRj nij Fij;t Þ ¼ dt j¼1 j¼1
ð2Þ
where i represents a single particle, j the particles contacted with particle i, m, V, I, R, v, and w the particle mass, volume, inertia moment, radius, linear velocity, and angular velocity, respectively, rpg the local pressure drop, Fd the drag force, Fg the gravitational force, Fij;n and Fij;t the normal and tangential components of the contact force from particle j to i, and Tij;t the torque. The contact force is calculated according to a linear spring-dashpot model where the force is a
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function of particle overlap and relative velocity. Details of the contact force model can be referred to Ref. [5]. Since a gas–solid system usually has a large number of particles, it is essential to optimize the strategy of particle collision detection. The present model employs the cell list and neighbor list techniques to speed up the search for particle collision. The drag force, Fd in Eq. (1), is calculated by Fd ¼
V ib ðu vi Þ ð1 eg Þ
ð3Þ
where u is the local gas velocity, eg the local gas volume fraction, and b inter-phase momentum transfer. The drag models frequently used in gas–solid fluidized beds [7], Ergun, Wen, Yu, De Felice, and Beetstra et al. models, are implemented in the developed model. During the present simulation, Ergun, Wen, and Yu drag model is adopted. The gas phase is treated as continuum and described by the volume-averaged Navier-Stokes equations. Mass and momentum conservations are @ ðeg qg Þ þ r ðeg qg uÞ ¼ S g @t @ ðeg qg uÞ þ r ðeg qg uuÞ @t ¼ eg rpg þ r ðeg sg Þ þ eg qg g Sm
ð4Þ
ð5Þ
where qg is the gas density, sg the gas viscous stress tensor, S g the gas mass source due to heterogeneous reactions, Sm the gas momentum source due to inter-phase interaction. For dense gas–solid flows in fluidized beds, two-way coupling is required. According to Newtonian third law, Sm in a fluid cell is determined by adding up the drag force of the particles located in the fluid cell. Sm ¼
Np 1 X
V cell
Fd
ð6Þ
k¼1
where V cell is the volume of the fluid cell. In the hydrodynamic DEM–CFD model, S g in Eq. (4) is set to zero. When it is extended to model of reacting gas–solid systems involved with heterogeneous reactions, S g should not be zero. However, the previous works [16–18] neglected this effect. In our model, S g due to heterogeneous reactions is considered which is introduced in the following. 2.2. Heat transfer The heat balance for an individual particle is given below: mi C p;i
dT i ¼ Qcv þ Qpp þ Qrad þ QR dt
ð7Þ
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where Qcv ; Qpp ; Qrad ; and QR represent gas– particle convective, particle–particle conduction, radiation heat transfer, and heterogeneous chemical reactions, respectively. Qcv is calculated by Qcv ¼ hcv Ai ðT g T i Þ, where the heat transfer coefficient hcv is determined by Ranz and Marshall correlation [9,17]. Qpp is calculated by the method used in Ref. [10]. For simplicity, Qrad is not considered in the present model. The conservation equation for the gas energy is @ ðeg qg C pg T g Þ þ r ðeg qg C pg uT g Þ @t ¼ r ðeg k g rT g Þ þ S Q;cv þ S Q;R þ S h
ð8Þ
where T g is the gas temperature, C pg the gas capacity, k g the gas thermal conductivity, S Q;cv the heat source due to gas–particle convective heat transfer, S Q;R the heat source due to chemical reactions, S h the heat transported by mass source of S g in Eq. (4). S Q;cv is calculated in a similar way of Sm in Eq. (5), S Q;cv ¼
Np 1 X
V cell
Qcv
ð9Þ
k¼1
S Q;R is determined by heat release of chemical reactions. S h is determined by the formation enthalpies carried along with the inter-phase transferred mass of S g in Eq. (4). The momentum transfer due to S g is not calculated since it is negligible. 2.3. Heterogeneous reactions Char particle oxidation reaction is considered. CO and CO2 are produced according to the following equation: k eff
C þ 0:5ð1 þ gÞO2 !ð1 gÞCO þ gCO2
ð10Þ
where g denotes the proportion of CO2 and its value is determined according to the experimental results by Refs. [19,20]. The “Shrinking Core – Constant Particle Size” model is adopted, in which the reaction surface moves into the char particle, leaving behind an ash layer. Thus, the effective char particle oxidation rate (k eff ) is controlled by three steps: diffusion of gaseous reactant from gas phase to the particle surface, diffusion of gas through the ash layer, and reaction of gas with char at the core surface. Due to a short simulation of 15 s in the present work, the variation in char core diameter is negligible, which permits that the resistance of diffusion of gas through the ash layer is neglected. Therefore, the effective char particle combustion rate is controlled by 1 1 1 ¼ þ k eff k kin hm
ð11Þ
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where k kin is kinetic rate at the char particle surface, and hm the mass transfer coefficient to particle surface. k kin is calculated by Arrhenius-type correlation [21]. k kin ¼ 595T p expðEA =Ru T p Þ
ð12Þ
hm is calculated by particle Sherwood number which is determined according to the study by Ref. [22]. The mass balance equation for the char particle is dmi ¼ k eff Ai C O2 dt
ð13Þ
where Ai is the particle surface area, and C O2 the molar concentration of O2. The mass balance for the gas species i is @ ðeg qg Y i Þ þ r ðeg qg uY i Þ @t ¼ r ðDi rY Þ þ S Yi
ð14Þ
where Y i is the mass-fraction of gas species i, Di its diffusion coefficient, and S Yi the net production rate of species i due to heterogeneous and homogeneous reactions. The heterogeneous reaction of Eq. (10) alters the gas continuity, and the mass source of Eq. (4) is determined by S g ¼ MW O2 x_ O2 þ MW CO x_ CO þ MW CO2 x_ CO2
ð15Þ
where MW O2 ; MW CO ; and MW CO2 are the molecular weight of O2, CO and CO2, respectively, and x_ O2 ; x_ CO ; and x_ CO2 the net volumetric production rate of O2, CO and CO2 in a fluid cell, respectively, which are calculated by mapping the char particle reaction to the fluid cells.
3.1. Computational condition All simulations are performed on a pseudo-3D fluidized bed with bed thickness of one particle diameter. The gas is introduced uniformly at the bed bottom and flows out of the bed at the top. At the gas inlet, the gas velocity and temperature are specified. At the outlet, the pressure-outlet boundary condition is adopted. At the walls, the no-slip wall condition for the gas phase is assumed and the heat flux zero. Table 1 lists details of the parameters for the simulated system. In different simulation cases, (a) two kinds of chars with activation energy in Eq. (12), EA = 149 106 J/kmol, 125 106 J/kmol, denoted as Char A and B, (b) three levels of temperature for initial and boundary conditions, T0 = 1123, 1173, 1223 K, (c) two kinds of mixtures of gas inlet, with propane-premixed (YO2 = 23%, YC3H8 = 3.74%, and YN2 = 73.26%) and without propane (YO2 = 23% and YN2 = 77%), denoted as gas A and B, are employed. In together, 12 cases are simulated. In all cases, both the CFD and DEM time steps are 0.0001 s. The gas–solid flow without chemical reactions is solved first. After basic flow pattern is established, the models of heat transfer and chemical reactions are activated, and the char particles located in the freeboard are freed. Then the simulation is performed for another physical 15 s. In the following sections, we present the combustion behaviors of the char particles and combustible gases, respectively, in comparison with findings from experimental studies in the literature. 3.2. Behaviors of char particles Figure 1 shows snapshots of the mixing pattern of the char particles for a typical condition (Char
2.4. Homogeneous reactions Propane (C3H8) combustion is considered. The reaction scheme adopts the four-step global kinetic mechanism proposed by Hautman et al. [23] C3 H8 ! 1:5C2 H4 þ H2 C2 H4 þ O2 ! 2CO þ 2H2 CO þ 0:5O2 ! CO2 H2 þ 0:5O2 ! H2 O
3. Results and discussion
ð16Þ ð17Þ ð18Þ ð19Þ
where the reaction rates and kinetic parameters are taken from Ref. [23]. The reaction rates, expressed as power functions of species molar concentration, may be infinite during computing. Program is designed to avoid such numerical problems. These stiff chemistry source terms are solved by the Runge–Kutta algorithm.
Table 1 The values of parameters for the simulation system. Bed size CFD cell size
16 80 cm2 0.8 1.6 cm2
Sand particle Diameter Number Density
1.5 mm 11,000 2600 kg/m3
Char particle Diameter Number Density Carbon/ash
1.5 mm 300 2200 kg/m3 70/30%
Gas Minimum fluidization velocity Inlet gas velocity
0.972 m/s at 1123 K 4 m/s for all cases
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Fig. 1. Snapshots at different times of mixing patterns for a typical condition (Char A, YC3H8 = 3.74%, T0 = 1173 K). The char particles are amplified by a factor of 5 for better observation. The yellow (weak color) particles represent bed particles, while black (strong color) particles chars. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
A, YC3H8 = 3.74%, T0 = 1173 K). The char particles located in the upper bed are freed at 2 s and fall down onto the dense bed surface, where the bubbles burst causing a strong solids back mixing. Then the chars move into the dense bed and follow the movement of the bed particles driven by the bubbles. After about 9 s, a well-mixed state of the chars is reached. The computation clearly demonstrates the intense solids mixing which is regarded as a special characteristic of fluidized beds. Figure 2 shows the total mass of carbon as a function of time under different conditions. The total mass of carbon is calculated by summing up the carbon mass contained in each of the char particles. In Fig. 2a, under propane-free atmosphere the reaction rate of Char A increases with increase in the bed temperature, and it decreases by adding propane into the gas. In Fig. 2b, for Char B under propane-free atmosphere its reaction rate keeps almost constant with increase in the bed temperature, while the reaction rate also decreases by adding propane into the gas. For better comparison of the results shown in Fig. 2, the total consumption mass of carbon related to its combustion time is calculated, yielding the average values of the char reaction rate. Figure 3 presents the char reaction rate under different conditions considered in Fig. 2. The reaction rate of Char B is much larger than that of Char A. Again, it can be clearly seen that under propane-free atmosphere the combustion rate of Char B keeps almost constant while Char A increases as the temperature rises. It indicates the reaction of Char B, with a lower value of activation energy, is controlled by mass transfer process. For both the chars, their combustion rates
Fig. 2. Total mass of carbon with time for various conditions. The total mass of carbon is calculated by summing up carbon mass within each individual char particle.
are decreased by premixing propane with the gas, because the propane competes for O2 with
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Fig. 3. Combustion rate of carbon for various conditions, calculated according to the data in Fig. 2.
the chars. Hesketh and Davidson [24] also observed the phenomena in their experimental investigations. Furthermore, the negative effect of the propane on the char reaction rate is more evident for Char B or at higher bed temperatures. A higher temperature promotes combustible gases to burn, but does not promote combustion of Char B since its reaction is controlled by mass transfer process. Thus, more amount of O2 is consumed by combustible gases within the bed at the higher temperature, reducing O2 available for the chars. Consequently, it happens that, although a bit of surprise at first glance, the combustion rate of Char B decreases as the bed temperature increases under propane-premixed atmosphere, which was found by Hesketh and Davidson [24]. 3.3. Behaviors of combustible gas The detailed combustion behaviors of gases can also be examined conveniently from the simulation results. An example is shown in Figure 4. It plots the mass-fraction profiles of gas species
Fig. 4. Gas species mass-fraction profiles along the bed height at 12 s for a typical condition (Char A, YC3H8 = 3.74%, T0 = 1173 K).
along the bed height at 12 s for the condition (Char A, YC3H8 = 3.74%, T0 = 1173 K). The combustion of C3H8 is almost completed below the height of 0.4 m. Within the reaction zone of C3H8, the reactants (C3H8 and O2) decrease along the height, the main product (CO2) increases, and the intermediate species (C2H4 and CO) first reach their peaks and then decrease. The presented results of the mass-fraction profiles of gas species are reasonable. Figure 5 compares the mass-fraction profiles of the main gas species (O2 and CO2) at different temperatures with Char A. As expected, the mass-fraction of O2 decreases as the temperature rises at the same bed height within the reaction zone of C3H8. It also gives an explanation for the variation of the char reaction rate presented in Fig. 3: O2 is consumed more within the dense bed as the temperature rises, leading to a decreased reaction rate of the char particles. The distribution of gaseous fuel combustion in fluidized beds has been investigated extensively [25,26]. In various experimental investigations, it seems that volatile combustion can take place significantly either above the bed surface, in rising bubbles, or inside the emulsion phase, which depends on the bed temperature [25]. Figure 6 plots the heat source generated from gas combustion for the conditions considered in Fig. 5. In the case of T0 = 1223 K, the heat source is intense within the dense bed, indicating the combustible gases are almost burned completely within a short distance above the distributor. For case T0 = 1173 K, a significant fraction of heat is released just above the bed surface, indicating less amount of gases are burned within the dense bed. When the temperature is further decreased, for case T0 = 1123 K, the phenomenon of intense heat release above the bed surface is more evident. Zukowski et al. [26] presented a insight into combustion of gaseous fuel in a fluidized bed. They obtained temperature fields in a fluidized
Fig. 5. Main gas species mass-fraction profiles of O2 and CO2 along height at 12 s at different temperatures of T0 = 1123, 1173, and 1223 K.
D. Liu et al. / Proceedings of the Combustion Institute 33 (2011) 2701–2708
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with bubbles. Figure 7a shows the instantaneous fluctuations of gas volume fraction at a computing cell, x = 7.6 cm and y = 5.6 cm, for the condition (Char A, YC3H8 = 3.74%, T0 = 1173 K); Fig. 7b accordingly shows the instantaneous heat source generated from two phase heat transfer, heterogeneous reactions, and homogeneous reactions. From the local structure, it can be found that the local heat source generated from the homogeneous reaction is dominant, and it fluctuates with gas volume fraction, suggesting the gas reaction is highly related with bubbles, which agrees with the visual measurements by Zukowski et al. [26]. 4. Conclusions Fig. 6. Contours of heat source generated from gas combustion at 12 s at different temperatures of T0 = 1123, 1173, and 1223 K.
bed burning a propane–air mixture by visual recording and RGB analysis, providing the direct proof that the local temperatures are associated
1. A comprehensive DEM–CFD model is developed for fluidized bed combustion. The model takes into account particle-scale heat transfer, homogeneous and heterogeneous reactions, as well as hydrodynamics of dense gas–solid flow in fluidized beds. The coupling between the gas continuity and heterogeneous reactions is addressed. 2. The developed model is used to simulate char and propane combustion in a fluidized bed. The phenomena observed from the simulation results are satisfying in various respects, e.g., (a) combustible gases reduce char combustion rate, especially for conditions with higher bed temperatures or highly reactive chars; (b) gas combustion takes place significantly above the bed surface, in rising bubbles, or inside the emulsion phase, depending on the bed temperature. 3. The results presented in this work clearly indicate the comprehensive DEM–CFD model can provide detailed local information as well as the macro structures at fluidized bed scale. It can play an important role in a multiscale strategy for fluidized bed combustion. Acknowledgments Financial supports of this work by National Key Technology R&D Program (2006BAA03 B02-10), the High-tech Research and Development Program of China(2009AA05Z311), and the Scientific Research Foundation of Graduate School of Southeast University are gratefully acknowledged. References
Fig. 7. Local fluctuations of instantaneous gas volume fraction and heat source due to two phase heat transfer, heterogeneous and homogeneous reaction, for a typical condition (Char A, YC3H8 = 3.74%, T0 = 1173 K) at a computing cell whose center position is x = 7.6 cm, y = 5.6 cm.
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